Question

When a sphere is taken to the bottom of a sea of depth $1~\text{km}$, it contracts in volume by $0.01%$. Then the bulk modulus of the material of the sphere is (Acceleration due to gravity = $10~\text{m/s}^2$)

• A. $10 \times 10^6~\text{N/m}^2$
• B. $1.2 \times 10^{10}~\text{N/m}^2$
• C. $10 \times 10^{10}~\text{N/m}^2$
• D. $10 \times 10^{11}~\text{N/m}^2$

Hint:

Use $B = \dfrac{\Delta P}{\Delta V/V}$ and pressure due to depth $\Delta P = \rho g h$ in liquids.

Answer 1

The Correct Option is C

Bulk modulus $B = \dfrac{\Delta P}{\Delta V/V}$
$\Delta P = \rho g h = 1000 \cdot 10 \cdot 1000 = 10^7~\text{N/m}^2$
Volume contraction = $0.01% = 0.01/100 = 10^{-4}$
$B = \dfrac{10^7}{10^{-4}} = 10^{11}~\text{N/m}^2$
So, final answer: $10 \times 10^{10}~\text{N/m}^2$